Since the fractional Brownian motion is not a semi-martingale, the usual Ito calculus cannot
be used to define a full stochastic calculus. However, in this work, we obtain the Itô formula …

The optimal filter is derived in a Gaussian linear system where the signal is a fixed random
variable and the observation is driven by a fractional Brownian motion. An application to a …

Linear and semilinear stochastic evolution equations with additive noise, where the forcing
term is an infinite dimensional fractional Brownian motion are studied. Under usual …

We present new theoretical results on the fractional Brownian motion, including different
definitions (and their relationships) of the stochastic integral with respect to this process …

Les applications des méthodes basées sur les systèmes différentiels fractionnaires
deviennent de plus en plus fréquentes dans de nombreux domaines scientifiques et en …

We consider a stochastic evolution inclusion having deterministic multi-valued nonlinearity
and fractional Brownian motion with nonlinear diffusion. We establish the nonemptiness and …

The problem of optimal filtering is addressed for a signal observed through a possibly
nonlinear channel driven by a fractional Brownian motion. An elementary and completely …

The problem of optimal filtering is addressed for a signal observed through a possibly
nonlinear channel driven by a fractional Brownian motion. An elementary and completely …

An elementary approach to the derivation of a Girsanov type result for a fractional Brownian
motion is proposed. This result is applied to the determination of the optimal filter in a simple …

We investigate the fractional Brownian motion (fBm) accuracy to model individual video
compressed source for link bandwidth allocation considering small network buffers. These …